Just an update, I sent a secured message regarding the issue and I received this piece of good news:
Dear Aaron,
I assure you that the Avios already posted to your
Executive Club account with British Airways are yours to
keep and use regardless of the status of your credit card
account. Those Avios are not lost or forfeited upon
closure of this credit card account. I apologize for the
incorrect information you had previously received
regarding this issue and I assure you that the information
I provided you is accurate.
If you have any further questions, please reply using the
Secure Message Center.
Thank you,
Jonathan Kane
E-mail Customer Service Representative
1-800-436-7927
Account is owned by Chase Bank USA, N.A. and may be
serviced by its affiliates.